Let be a semigroup.
is left cancellative if, for all ,
is right cancellative if, for all ,
is cancellative if it is both left and right cancellative.
1 Relationship to some other types of semigroup
This is a generalisation of groups, and in fact being cancellative is a necessary condition for a semigroup to be embeddable in a group.
Note that a non-empty semigroup is a group if and only if it is cancellative and regular.
is weakly cancellative if, for all ,
A semigroup is completely simple if and only if it is weakly cancellative and regular.
2 Individual elements
An element is called left cancellative if, for all ,
An element is called right cancellative if, for all ,
|Date of creation||2013-03-22 14:25:09|
|Last modified on||2013-03-22 14:25:09|
|Last modified by||yark (2760)|
|Defines||weakly cancellative semigroup|
|Defines||left cancellative semigroup|
|Defines||right cancellative semigroup|